An algebraic continuous time parameter estimation for a sum of sinusoidal waveform signals

Rosane Ushirobira (1, 2) , Wilfrid Perruquetti (3, 1, 4) , Mamadou Mboup (1, 5)

1 NON-A - Non-Asymptotic estimation for online systems
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 Centrale Lille
4 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
5 CRESTIC - Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804

In this paper, a novel algebraic method is proposed to estimate amplitudes, frequencies, and phases of a biased and noisy sum of complex exponential sinusoidal signals. The resulting parameter estimates are given by original closed formulas, constructed as integrals acting as time-varying filters of the noisy measured signal. The proposed algebraic method provides faster and more robust results, compared with usual procedures. Some computer simulations illustrate the efficiency of our method.

Mots clés: Noise; Differential algebra; Sinusoidal wave; Parameter identification

Domaines: Automatique / Robotique

Rosane Ushirobira, Wilfrid Perruquetti, Mamadou Mboup. An algebraic continuous time parameter estimation for a sum of sinusoidal waveform signals. International Journal of Adaptive Control and Signal Processing, 2016, 30 (12), pp.1689-1713. ⟨10.1002/acs.2688⟩. ⟨hal-01342210⟩